diff --git a/base/broadcast.jl b/base/broadcast.jl
index 603f8ec54efc29..3950f24837835d 100644
--- a/base/broadcast.jl
+++ b/base/broadcast.jl
@@ -239,12 +239,6 @@ broadcast_indices
 # special cases defined for performance
 broadcast(f, x::Number...) = f(x...)
 @inline broadcast(f, t::NTuple{N,Any}, ts::Vararg{NTuple{N,Any}}) where {N} = map(f, t, ts...)
-@inline broadcast!(::typeof(identity), x::AbstractArray{T,N}, y::AbstractArray{S,N}) where {T,S,N} =
-    Base.axes(x) == Base.axes(y) ? copyto!(x, y) : _broadcast!(identity, x, y)
-
-# special cases for "X .= ..." (broadcast!) assignments
-broadcast!(::typeof(identity), X::AbstractArray, x::Number) = fill!(X, x)
-broadcast!(f, X::AbstractArray, x::Number...) = (@inbounds for I in eachindex(X); X[I] = f(x...); end; X)
 
 ## logic for deciding the BroadcastStyle
 # Dimensionality: computing max(M,N) in the type domain so we preserve inferrability
@@ -261,7 +255,7 @@ longest(::Tuple{}, ::Tuple{}) = ()
 # combine_styles operates on values (arbitrarily many)
 combine_styles(c) = result_style(BroadcastStyle(typeof(c)))
 combine_styles(c1, c2) = result_style(combine_styles(c1), combine_styles(c2))
-combine_styles(c1, c2, cs...) = result_style(combine_styles(c1), combine_styles(c2, cs...))
+@inline combine_styles(c1, c2, cs...) = result_style(combine_styles(c1), combine_styles(c2, cs...))
 
 # result_style works on types (singletons and pairs), and leverages `BroadcastStyle`
 result_style(s::BroadcastStyle) = s
@@ -445,11 +439,36 @@ Note that `dest` is only used to store the result, and does not supply
 arguments to `f` unless it is also listed in the `As`,
 as in `broadcast!(f, A, A, B)` to perform `A[:] = broadcast(f, A, B)`.
 """
-@inline broadcast!(f, C::AbstractArray, A, Bs::Vararg{Any,N}) where {N} =
-    _broadcast!(f, C, A, Bs...)
+@inline broadcast!(f::Tf, dest, As::Vararg{Any,N}) where {Tf,N} = broadcast!(f, dest, combine_styles(As...), As...)
+@inline broadcast!(f::Tf, dest, ::BroadcastStyle, As::Vararg{Any,N}) where {Tf,N} = broadcast!(f, dest, nothing, As...)
+
+# Default behavior (separated out so that it can be called by users who want to extend broadcast!).
+@inline function broadcast!(f, dest, ::Void, As::Vararg{Any, N}) where N
+    if f isa typeof(identity) && N == 1
+        A = As[1]
+        if A isa AbstractArray && Base.axes(dest) == Base.axes(A)
+            return copy!(dest, A)
+        end
+    end
+    return _broadcast!(f, dest, As...)
+end
+
+# Optimization for the all-Scalar case.
+@inline function broadcast!(f, dest, ::Scalar, As::Vararg{Any, N}) where N
+    if dest isa AbstractArray
+        if f isa typeof(identity) && N == 1
+            return fill!(dest, As[1])
+        else
+            @inbounds for I in eachindex(dest)
+                dest[I] = f(As...)
+            end
+            return dest
+        end
+    end
+    return _broadcast!(f, dest, As...)
+end
 
-# This indirection allows size-dependent implementations (e.g., see the copying `identity`
-# specialization above)
+# This indirection allows size-dependent implementations.
 @inline function _broadcast!(f, C, A, Bs::Vararg{Any,N}) where N
     shape = broadcast_indices(C)
     @boundscheck check_broadcast_indices(shape, A, Bs...)
diff --git a/base/sparse/higherorderfns.jl b/base/sparse/higherorderfns.jl
index 4f90b7bc6a4304..c287342c5bdaad 100644
--- a/base/sparse/higherorderfns.jl
+++ b/base/sparse/higherorderfns.jl
@@ -93,7 +93,8 @@ end
 # (3) broadcast[!] entry points
 broadcast(f::Tf, A::SparseVector) where {Tf} = _noshapecheck_map(f, A)
 broadcast(f::Tf, A::SparseMatrixCSC) where {Tf} = _noshapecheck_map(f, A)
-function broadcast!(f::Tf, C::SparseVecOrMat) where Tf
+
+@inline function broadcast!(f::Tf, C::SparseVecOrMat, ::Void) where Tf
     isempty(C) && return _finishempty!(C)
     fofnoargs = f()
     if _iszero(fofnoargs) # f() is zero, so empty C
@@ -106,14 +107,18 @@ function broadcast!(f::Tf, C::SparseVecOrMat) where Tf
     end
     return C
 end
-function broadcast!(f::Tf, C::SparseVecOrMat, A::SparseVecOrMat, Bs::Vararg{SparseVecOrMat,N}) where {Tf,N}
-    _aresameshape(C, A, Bs...) && return _noshapecheck_map!(f, C, A, Bs...)
-    Base.Broadcast.check_broadcast_indices(axes(C), A, Bs...)
-    fofzeros = f(_zeros_eltypes(A, Bs...)...)
-    fpreszeros = _iszero(fofzeros)
-    return fpreszeros ? _broadcast_zeropres!(f, C, A, Bs...) :
-                        _broadcast_notzeropres!(f, fofzeros, C, A, Bs...)
+@inline function broadcast!(f::Tf, dest::SparseVecOrMat, ::Void, As::Vararg{Any,N}) where {Tf,N}
+    if f isa typeof(identity) && N == 1
+        A = As[1]
+        if A isa Number
+            return fill!(dest, A)
+        elseif A isa AbstractArray && Base.axes(dest) == Base.axes(A)
+            return copy!(dest, A)
+        end
+    end
+    return spbroadcast_args!(f, dest, Broadcast.combine_styles(As...), As...)
 end
+
 # the following three similar defs are necessary for type stability in the mixed vector/matrix case
 broadcast(f::Tf, A::SparseVector, Bs::Vararg{SparseVector,N}) where {Tf,N} =
     _aresameshape(A, Bs...) ? _noshapecheck_map(f, A, Bs...) : _diffshape_broadcast(f, A, Bs...)
@@ -1006,26 +1011,26 @@ Broadcast.BroadcastStyle(::SparseMatStyle, ::Broadcast.DefaultArrayStyle{N}) whe
 broadcast(f, ::PromoteToSparse, ::Void, ::Void, As::Vararg{Any,N}) where {N} =
     broadcast(f, map(_sparsifystructured, As)...)
 
-# ambiguity resolution
-broadcast!(::typeof(identity), dest::SparseVecOrMat, x::Number) =
-    fill!(dest, x)
-broadcast!(f, dest::SparseVecOrMat, x::Number...) =
-    spbroadcast_args!(f, dest, SPVM, x...)
-
 # For broadcast! with ::Any inputs, we need a layer of indirection to determine whether
 # the inputs can be promoted to SparseVecOrMat. If it's just SparseVecOrMat and scalars,
 # we can handle it here, otherwise see below for the promotion machinery.
-broadcast!(f, dest::SparseVecOrMat, mixedsrcargs::Vararg{Any,N}) where N =
-    spbroadcast_args!(f, dest, Broadcast.combine_styles(mixedsrcargs...), mixedsrcargs...)
-function spbroadcast_args!(f, dest, ::Type{SPVM}, mixedsrcargs::Vararg{Any,N}) where N
+function spbroadcast_args!(f::Tf, C, ::SPVM, A::SparseVecOrMat, Bs::Vararg{SparseVecOrMat,N}) where {Tf,N}
+    _aresameshape(C, A, Bs...) && return _noshapecheck_map!(f, C, A, Bs...)
+    Base.Broadcast.check_broadcast_indices(axes(C), A, Bs...)
+    fofzeros = f(_zeros_eltypes(A, Bs...)...)
+    fpreszeros = _iszero(fofzeros)
+    return fpreszeros ? _broadcast_zeropres!(f, C, A, Bs...) :
+                        _broadcast_notzeropres!(f, fofzeros, C, A, Bs...)
+end
+function spbroadcast_args!(f::Tf, dest, ::SPVM, mixedsrcargs::Vararg{Any,N}) where {Tf,N}
     # mixedsrcargs contains nothing but SparseVecOrMat and scalars
     parevalf, passedsrcargstup = capturescalars(f, mixedsrcargs)
     return broadcast!(parevalf, dest, passedsrcargstup...)
 end
-function spbroadcast_args!(f, dest, ::PromoteToSparse, mixedsrcargs::Vararg{Any,N}) where N
+function spbroadcast_args!(f::Tf, dest, ::PromoteToSparse, mixedsrcargs::Vararg{Any,N}) where {Tf,N}
     broadcast!(f, dest, map(_sparsifystructured, mixedsrcargs)...)
 end
-function spbroadcast_args!(f, dest, ::Any, mixedsrcargs::Vararg{Any,N}) where N
+function spbroadcast_args!(f::Tf, dest, ::Any, mixedsrcargs::Vararg{Any,N}) where {Tf,N}
     # Fallback. From a performance perspective would it be best to densify?
     Broadcast._broadcast!(f, dest, mixedsrcargs...)
 end